Properties

Label 12870.bh
Number of curves $2$
Conductor $12870$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bh1")
 
E.isogeny_class()
 

Elliptic curves in class 12870.bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12870.bh1 12870bg1 \([1, -1, 1, -3805973, 2953734581]\) \(-225817164626811885218547/8821617915914375000\) \(-238183683729688125000\) \([3]\) \(544320\) \(2.6790\) \(\Gamma_0(N)\)-optimal
12870.bh2 12870bg2 \([1, -1, 1, 18669337, 9273598417]\) \(36561089342650869429237/23047447204589843750\) \(-453642903327941894531250\) \([]\) \(1632960\) \(3.2283\)  

Rank

sage: E.rank()
 

The elliptic curves in class 12870.bh have rank \(0\).

Complex multiplication

The elliptic curves in class 12870.bh do not have complex multiplication.

Modular form 12870.2.a.bh

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} - q^{7} + q^{8} - q^{10} + q^{11} + q^{13} - q^{14} + q^{16} - q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.